How can I improve the realism of my pencil texture lines in freestyle?
According to the wiki article Textured Strokes the Use Tips option is available when Along Strokes mapping is used:


  Along Strokes Means that the texture will be drawn along the stroke length, making it possible to mimick pencil or brush marks.


However by default it won't really make any much difference:



The option depends on spacing between strokes mapped to the geometry:


  Along Stroke mapping depends by the LineStyle spacing parameter that can be found in the linestyle settings. It sets how much the texture will be stretched along the stroke length. Higher spacing means less tiling. 


It can be found in the same place where strokes are set up to use texture, Render Layers tab > Freestyle Linestyle rollout > Texture panel:



With that texture rendered strokes become more smeared:


Spacing was set to 5

The effect however is still a bit off as its thickness is not varying and the stamp still is present.

From here on settings from the teapot file were used as reference as well  

To correct that don't use thickness of 20; in fact less than 10 will be enough. For convincing and effective results better to let it draw with thin line and repeat it 2 or more times; that will simulate effect of graphite or a pencil strokes more nicely. 
This is the result wil Stroke effect decreaed to 6:

 

Now some repeating pencil strokes would add a bit of "realism" to the image. With Repeat set to 3 it will be already more or less good. But to add even more to that in the Geometry panel add Spatial Noise modifier.

 

What the modifier does is it varies strokes created by the Repeat option. Amplitude option will increase or decrease how far away the repeated lines are from original; Scale adjusts the scale of repeated detail (if it was at 15 you'd get step-like corners around the line).

Smeared chalk like effect can be created with Along Stroke modifier added to the Thickness panel. According to the manual it applies gradient along each stroke while substituting original values of the line. To make lines more fat and smeared Use Tips option can also be unchecked (in this case):



The partially transparent effect from the teapot scene is created with adding Along Stroke modifier in the Alpha panel, but for some reason in Cycles it isn't visible (teapot scene is in Internal). Even setting Thickness to 0 doesn't really change anything, which is quite unexpected. It looks like in Cycles the freestyle won't calculate and hence use alpha of the charcoal texture. If making that in Internal effect shows up immediately:

 

It's hard to say if this means for you that Freestyle went ahead since that time but anyway the resulting effect of the freestyle strokes can be changed quite drastically by editing options and adding modifiers.



If going with only one round of the stroke (and hence only one stroke drawn on the objects) you will need to alter it as much as possible in order to get varying style. You can use several line styles as already mentioned by @TK or you can go with more modifiers for one line style.
I will use modifiers for Thickness panel mostly but possibilities are nearly endless as many of them have also additional modes of stroke overlaying which changes end result quite noticeable.  

Note: 


there aren't any modifiers on the line style for this one; none of the results used from the several rounds above.
in all the results here Face Smoothness in the Render Layers tab > Freestyle rollout is used for using smooth shading of the mesh.
It also means that shading of the meshes should be set to smooth as well.
in all the results here Alpha Fac in the Line Style Output node in the line style setup is set to 0.5. This allows Cycles to overlay alpha of the texture and use it along with the base color. For some reason it also fixes usage of the modifiers in the Alpha panel. None of these is needed in Blender Internal.  


Using stroke thickness (Freestyle Line Style > Thickness) at 3 and Spacing at 1 the result is thin drawing:



To increase the variation add Along Stroke modifier to the thickness of the stroke. It will apply new values for thickness based on the progression type and blending mode choosed; from the manual:


  The Along Stroke modifier alters the base thickness with a new one from either a linear progression or a custom curve, mapped along each stroke’s length. In other words, it applies the selected progression along each stroke.




To mimic caligraphic changing of the line thickness which depends on the stroke angle add Caligraphy modifier. Its  Orientation property will simullate orientaition of the virtual pen drawing on the paper - the more it's aligned with the vertical axis the more horizontal strokes will be fat and vertical - thin. Default values of 60 are quite good as well.



Also it's possible to add some noise to the stroke in general; Noise modifier will be the last in the Thickness panel.



To simulate transparency of the strokes modifiers in the Alpha panel are added. In this example Along Stroke modifier is used. 



Note also that most of the modifiers can be set to another blending modes thus altering their final result which allows even more different things to try.